Problem: Solve for $x$ : $5x^2 + 15x - 90 = 0$
Solution: Dividing both sides by $5$ gives: $ x^2 + {3}x {-18} = 0 $ The coefficient on the $x$ term is $3$ and the constant term is $-18$ , so we need to find two numbers that add up to $3$ and multiply to $-18$ The two numbers $-3$ and $6$ satisfy both conditions: $ {-3} + {6} = {3} $ $ {-3} \times {6} = {-18} $ $(x {-3}) (x + {6}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -3) (x + 6) = 0$ $x - 3 = 0$ or $x + 6 = 0$ Thus, $x = 3$ and $x = -6$ are the solutions.